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Factorization of polynomials over finite fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mceliece, Robert J. |
| Copyright Year | 1969 |
| Abstract | If f(x) is a polynomial over GF(q), we observe (as has Berlekamp) that if h(x)2 =_h(x) (modf(x)), thenf(x) = IHa eGF(q) gcd (f(x), h(x) a). The object of this paper is to give an explicit construction of enough such h's so that the repeated application of this result will succeed in separating all irreducible factors of f. The h's chosen are loosely defined by hi(x) = xi + xiq + xiq2 + * * * (mod f(x)). A detailed example over GF(2) is given, and a table of the factors of the cyclotomic polynomials 4b(x) (mod p) for p = 2, n < 250; p = 3, n < 100; p = 5, 7, n < 50, is included. |
| Starting Page | 861 |
| Ending Page | 867 |
| Page Count | 7 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0025-5718-1969-0257039-X |
| Volume Number | 23 |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1969-23-108/S0025-5718-1969-0257039-X/S0025-5718-1969-0257039-X.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0025-5718-1969-0257039-X |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
